In a coconut grove,$(x+2)$ trees yield $60$ nuts per year,$x$ trees yield $120$ nuts per year,and $(x-2)$ trees yield $180$ nuts per year. If the average yield per year per tree is $100$,find the value of $x$.

$A$ man spends on an average $Rs. 269.47$ for the first $7$ months and $Rs. 281.05$ for the next $5$ months. Find out his monthly salary if he saved $Rs. 308.46$ during the year. (in $Rs.$)

The average marks of students in an examination was $65$. It was later found that the marks of one student had been wrongly entered as $83$ instead of $38$. If there were $50$ students, what is the correct average?

The average age of $5$ members is $21 \text{ years}$. If the age of the youngest member is $5 \text{ years}$,find out the average age of the family at the birth of the youngest member (in $\text{years}$).

The average of marks obtained by $150$ candidates in a certain examination is $50$. If the average marks of passed candidates is $55$ and that of the failed candidates is $25$,what is the number of candidates who passed the examination?

The average monthly expenditure of a family for the first four months is $Rs. 2750$,for the next three months is $Rs. 2940$,and for the last five months is $Rs. 3130$. If the family saves $Rs. 5330$ throughout the year,find the average monthly income of the family for that year (in $Rs.$).